Question

solve by applying the zero prod
$405p^2 - 125 = 0$
if there is more than one solution

Explanation:

Step1: Isolate the \( p^2 \) term

First, we add 125 to both sides of the equation \( 405p^2 - 125 = 0 \) to get \( 405p^2 = 125 \). Then, we divide both sides by 405 to isolate \( p^2 \), so \( p^2=\frac{125}{405} \). We can simplify this fraction by dividing both the numerator and the denominator by 5, which gives \( p^2 = \frac{25}{81} \).

Step2: Take the square root of both sides

Now, we take the square root of both sides. Remember that when we take the square root of a number, we get both a positive and a negative solution. So, \( p=\pm\sqrt{\frac{25}{81}} \). Since \( \sqrt{25} = 5 \) and \( \sqrt{81}=9 \), we have \( p = \pm\frac{5}{9} \).

Answer:

\( p=\frac{5}{9} \) or \( p = -\frac{5}{9} \)